Bending-active inflated shells: a review of semi-analytical approaches for global behavior modeling

Bending-active inflated shells represent a novel class of lightweight deployable structures, typically composed of modular inflatable cushions combined with auxiliary cables and cross-bracing. Their global behavior relies on a self-erecting mechanism in which active bending, induced by cable tensioning, provides stability and load-carrying capacity. This structural system has been explored theoretically through analogies with the classical elastica problem, offering valuable insights into its geometric and mechanical characteristics. Subsequent extensions of semi-analytical formulations allowed the inclusion of external point loading conditions, although initial models were restricted to shapes without inflection points. Recent methodological advances have overcome these limitations, enabling the description of a broader class of deformed configurations and thus widening the potential applicability of semi-analytical models for such systems. This paper presents a review of semi-analytical approaches to modeling the global behavior of bending-active inflated shell structures. Selected contributions from the literature are mentioned to contextualize existing approaches, highlighting their assumptions and reported limitations. Particular emphasis is placed on the potential of semi-analytical frameworks to provide physically interpretable results that complement numerical simulations and experimental studies. Finally, research gaps and future directions are outlined, including the need for formulations capable of capturing material nonlinearities, interaction effects, and scale-dependent phenomena.